Dear Michael

If I understand you correctly, you already have an estimate of the
measurement error? It would seem that if you can estimate the error, then
this estimate comes with a standard error.

For example, suppose that you have a nonlinear model where one of the
predictors is a sum of two variables, which has been measured with error.
You then want to use simex to extrapolate the value the estimator of the
nonlinear model would have if there were no error. If these two variables
are related according to a factor model, then the measurement error estimate
would be the correlation between the variables, with the corresponding s.e.
(assuming the reliabilities of the variables are equal). It depends of
course what the measurement model and corresponding estimates are but you
usually get a standard error with the estimate.

If you want to take into account the variability in this estimate, in the
case of simex an approach would be to simulate values of the measurement
error estimates from its distribution using the standard error, and repeat
the simex procedure each time. You are then in the framework of multiple
imputation. So you need to record the between- and within- variance and
covariance of the estimates, and then combine them according to the rules
laid out by Rubin to get the final variance of the nonlinear model's
estimates. The between covariance matrix you get from the simulations. The
within covariance matrix as I understood from the book needs to be
bootstrapped.

So it is quite a process but certainly possible!

-daniel

P.S.   Note that simex is an approximate method; if you possibly can use
them, the alternative likelihood based or estimating equations approaches
provide a method of correcting the standard errors for uncertainty in the
measurement error estimates. This is explained in the book by Carroll,
Ruppert & Stefanski, in the appendix.



On Jan 28, 2008 2:36 AM, Michael Kubovy <kubovy@virginia.edu> wrote:

> Dear R-helpers,
>
> It is not clear to me how you get measurement.error SD when you have a
> single dataset, and it is not clear to me how sensitive SIMEX is to
> errors in the estimates of measurement error.
>
> Could someone please point me to the relevant literature?
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